@*****************************************************@
@         czt.gss - supplementary program to          @
@                                                     @
@         "Introduction to FFT in Finance"            @
@                                                     @
@      (c) 2004 Ales Cerny, all rights reserved       @
@*****************************************************@

/* procedure czt implements the chirp-z transform for short output lengths */

proc czt(x,m,w,A);
local n,nnew,b,fa,fb,chirp;
n=rows(x);
if m > n;
    print "choose m lower than or equal to the dimension of input vector";
    retp();
else;
nnew=optn(n);
chirp=A*w^(-seqa(0,1,n)^2/2);
b=chirp|zeros(2*nnew-2*n+1,1)|rev(chirp[2:n]);
fb=ffti(b^-1);
fa=ffti((x.*chirp)|zeros(2*nnew-n,1));
b=fftn(fa.*fb);
retp(chirp[1:m].*b[1:m]);
endif;
endp;